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Title: Cosmological histories in bimetric gravity: a graphical approach

Abstract

The bimetric generalization of general relativity has been proven to be able to give an accelerated background expansion consistent with observations. Apart from the energy densities coupling to one or both of the metrics, the expansion will depend on the cosmological constant contribution to each of them, as well as the three parameters describing the interaction between the two metrics. Even for fixed values of these parameters can several possible solutions, so called branches, exist. Different branches can give similar background expansion histories for the observable metric, but may have different properties regarding, for example, the existence of ghosts and the rate of structure growth. In this paper, we outline a method to find viable solution branches for arbitrary parameter values. We show how possible expansion histories in bimetric gravity can be inferred qualitatively, by picturing the ratio of the scale factors of the two metrics as the spatial coordinate of a particle rolling along a frictionless track. A particularly interesting example discussed is a specific set of parameter values, where a cosmological dark matter background is mimicked without introducing ghost modes into the theory.

Authors:
 [1]
  1. Oskar Klein Centre, Stockholm University, Albanova University Center 106 91 Stockholm (Sweden)
Publication Date:
OSTI Identifier:
22680008
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 02; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL CONSTANT; COUPLING; ENERGY DENSITY; EXPANSION; GENERAL RELATIVITY THEORY; GRAVITATION; INTERACTIONS; MATHEMATICAL SOLUTIONS; METRICS; NONLUMINOUS MATTER; PARTICLE TRACKS; PARTICLES

Citation Formats

Mörtsell, E., E-mail: edvard@fysik.su.se. Cosmological histories in bimetric gravity: a graphical approach. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/02/051.
Mörtsell, E., E-mail: edvard@fysik.su.se. Cosmological histories in bimetric gravity: a graphical approach. United States. doi:10.1088/1475-7516/2017/02/051.
Mörtsell, E., E-mail: edvard@fysik.su.se. Wed . "Cosmological histories in bimetric gravity: a graphical approach". United States. doi:10.1088/1475-7516/2017/02/051.
@article{osti_22680008,
title = {Cosmological histories in bimetric gravity: a graphical approach},
author = {Mörtsell, E., E-mail: edvard@fysik.su.se},
abstractNote = {The bimetric generalization of general relativity has been proven to be able to give an accelerated background expansion consistent with observations. Apart from the energy densities coupling to one or both of the metrics, the expansion will depend on the cosmological constant contribution to each of them, as well as the three parameters describing the interaction between the two metrics. Even for fixed values of these parameters can several possible solutions, so called branches, exist. Different branches can give similar background expansion histories for the observable metric, but may have different properties regarding, for example, the existence of ghosts and the rate of structure growth. In this paper, we outline a method to find viable solution branches for arbitrary parameter values. We show how possible expansion histories in bimetric gravity can be inferred qualitatively, by picturing the ratio of the scale factors of the two metrics as the spatial coordinate of a particle rolling along a frictionless track. A particularly interesting example discussed is a specific set of parameter values, where a cosmological dark matter background is mimicked without introducing ghost modes into the theory.},
doi = {10.1088/1475-7516/2017/02/051},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 02,
volume = 2017,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}
  • We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Einstein gravity.
  • We obtain the general cosmological evolution equations for a classically consistent theory of bimetric gravity. Their analytic solutions are demonstrated to generically allow for a cosmic evolution starting out from a matter dominated FLRW universe and relaxing towards a de Sitter (anti-de Sitter) phase at late cosmic time. In particular, we examine a subclass of models which contain solutions that are able to reproduce the expansion history of the cosmic concordance model inspite of the nonlinear couplings of the two metrics. This is demonstrated explicitly by fitting these models to observational data from Type Ia supernovae, Cosmic Microwave Background andmore » Baryon Acoustic Oscillations. In the appendix we comment on the relation to massive gravity.« less
  • A ghost-free theory of gravity with two dynamical metrics both coupled to matter is shown to be consistent and viable. Its cosmological implications are studied, and the models, in particular in the context of partially massless gravity, are found to explain the cosmic acceleration without resorting to dark energy.
  • We find the general conditions for viable cosmological solution at the background level in bigravity models. Furthermore, we constrain the parameters by comparing to the Union 2.1 supernovae catalog and identify, in some cases analytically, the best fit parameter or the degeneracy curve among pairs of parameters. We point out that a bimetric model with a single free parameter predicts a simple relation between the equation of state and the density parameter, fits well the supernovae data and is a valid and testable alternative to ΛCDM. Additionally, we identify the conditions for a phantom behavior and show that viable bimetricmore » cosmologies cannot cross the phantom divide.« less
  • In the framework of the bimetric theory of gravitation a homogeneous isotropic cosmological model is set up having negative spatial curvature (k=-1) and containing matter having negligible pressure. The solutions of the field equations are obtained as expansions in powers of a small parameter, the present value of which can be determined, in principle, from observational data. It appears that its order of magnitude is such that the PPN parameter ..cap alpha../sub 2/ considered by Lee et al. is small enough to make the bimetric theory viable. The rate of change with time of the gravitational constant is found tomore » be considerably smaller than the present estimated upper limit.« less